3. Suppose a person’s fortune is f = $1000, and his utility function is log(f). Suppose this person can buy tickets on the mutually exclusive events A1, A2 and A3 with prices x1 = 1/6, x2 = 1/3 and x3 = 1/2. Suppose this person’s probabilities on these three events are, respectively q1 = 1/2, q2 = 1/3 and q3 = 1/6.

(a) How much should such a person invest in each kind of ticket to maximize his expected utility?

(b) How many tickets of each kind should he buy?